Firearms in general are more intuitive, even those which require training to use. The bullet, in theory, should travel a fairly straight line towards the target, or beyond it. It will be fastest immediately outside of the barrel, and will lower and slow until it is stopped.

Bows have many more factors to consider. The arrows may travel in an arc, the bows require greater physical strength, they are hard to use while laying prone, the arrows may break, etc.

Muskets also deliver a heck of a whallop (Whereas Confederate Carl may remain in the fight with an arrow in his leg, a .60" ball will devastate his leg so badly I doubt he'd be walking again.)

In the 1500 and 1600's, many Native American warriors were noted for use of bows as, indeed, they were deadlier in the hands of a skilled (That's a very important part!) warrior than contemporary firearms. However, firearm technology advanced sufficiently by the 1800's to make the slowness of firing well worth it in ballistic power, range(!), the capacity to blow through cover, and ease of use.

Military doctrine in the civil war also lent itself well to the muskets, as the American militaries tended to shy away from guerilla attacks where the reduced range but higher rate of fire of bows and arrows is best accentuated.

((Similar stories may be observed historically, as to why guns as a technology were even advanced at all, when the ancient examples seem so poor in comparison to crossbows. Ease of use, less need for space, greater "whallop", easier to use while wounded or in cramped quarters, and easy to predict flight path. Later, range and accuracy would come, but those weren't dreadfully important in a European style conflict where masses of troops were king.))

Hope this helps!

This gets to why firearms replaced bows in warfare in general, especially since it happened well before firearms were at a level of capability to make the switch a no-brainer. If you were to pit an individual expert archer versus an individual rifleman from the 1860s against one another it would likely be a very close contest.

But wars have a lot of dynamics beyond individual battles and beyond individual warrior vs. warrior conflicts as well. In war logistics is hugely important, which is where firearms really show their advantages. Bows and arrows are more production limited than guns, powder, and bullets. Bow staves and arrow shafts come from trees and sometimes require special wood. They also require a considerable amount of individual craftsmanship to work. Arrowheads are fairly easy to make but fletching arrows properly is a very labor intensive task starting from raising and plucking the fowl (typically geese) up through making the arrows and even down to hauling the arrows around a battlefield (I'll return to that point shortly). Additionally, training good archers was a difficult and, again, manpower intensive task. In the case of, say, the English forces during the late middle ages it required keeping essentially a standing army of highly trained archers as well as constantly being geared up for bow and arrow production.

Firearms also have some other characteristic differences with bows that give them some key tactical advantages. Firearms are more resilient in damp conditions. In pre-industrial times warfare often was more restricted to the non-winter months, as that changed (due to, for example, the ability to bring huge quantities of supplies over long distances via rail) the necessity to be able to fight in adverse weather conditions became more of a priority. Also, whereas long distance arrow volley fire tends to come mostly from above, bullet volleys tend to come horizontally. These are harder to protect from, more dangerous, and due to their faster travel time more difficult to prepare for. If an arrow in a volley misses a target it'll hit the ground instead, if a bullet in a volley misses the first rank of soldiers it will continue and has the potential to hit any of the other soldiers behind. This makes volley firearms fire at close range absolutely devastating to a degree that arrows are not. Especially considering that it's often possible to sustain an arrow injury and continue fighting (or at least retain mobility) whereas the same is generally not true of large caliber musket/rifle fire which has a tendency to shatter bones.

Add to that the bayonet, which makes a musket or rifle into a somewhat effective pole arm at ranges where the low firing rates of a few per minute are no longer useful. Archers alone are almost never a complete battlefield unit, they need to be married to other units in order to actually hold or take ground. A group of soldiers armed with muskets or rifles with bayonets, however, is a complete unit. It may be supplemented with other forces such as artillery or cavalry, but it is capable of going onto the battlefield and taking or holding ground on its own.

Additionally, cannons were unarguably superior battlefield weapons with no equal for centuries. Because they share the use of gunpowder with handheld firearms there is a degree of synergy there in terms of logistics of production and supply. In need a unit could cast their own bullets in the field, as it were, as long as they had a supply of lead (which can be melted using camp fires and cast using hand-held molds).

Overall, a group of riflemen was easier to build (through conscription and short training), more convenient to supply (needing primarily food and gunpowder), more effective under more conditions, capable of being effective on their own without support from specialized units, and generally capable of more devastating attacks than archers were (volley firearms fire backed up by a bayonet charge). That's why firearms had come to dominate even starting in the 17th and 18th centuries and by the mid 19th century were well cemented as the most important weapon for fighting a modern battle.